一様な磁場を横切る電導性流体の管内振動流れII 平行平面完全導体壁間内の場合

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A theoretical analysis is developed for the oscillatory flow of an incompressible conducting viscous fluid through a channel with perfect electrical conductivity in a uniform transverse magnetic field under magnetohydrodynamic approximations. It is assumed that the pressure gradient is harmonically oscillating, and that the velocity and the induced fields have the same forms as the pressure gradient depends on time. Then we get the generalized solutions containing the limiting cases of the oscillating flow of viscous fluids, and of the steady flow of conducting fluids through the channel with perfect conductivity.　Numerical calculations given by the relations of velocity, Poiseuille number and induced fields with Hartmann number, the oscillatory Reynolds number and wall conductivity are discussed. Magnetohydrodynamic effects that the inverse of Poiseuille number decreases, whenever the Hartmann number is increased, is more remarkable in the case of perfect conducting walls than in the case of the insulating ones　When the Hartmann number is small, the amplitude of the velocity has axial-symmetrical, two definite maxima near the walls, but when the Hartmann number is large, it becomes flat, that is, the annular effects of Richardson and Tyler is decreased by magnetohydrodynamic interaction. The shifting phase is always smaller in the perfect conducting channel than in the insulating one.　When a certain electrically conducting fluid is oscillated through a channel with perfect conductivity, it is accelerated as its being done by an electromagnetic pump. In this phenomenon it is pointed out that magnetic Prandtl number is the important factor as much as Hartmann number and oscillatory Reynolds number in order to choose such a fluid.
山形大学の論文
1969-03-20

一様な磁場を横切る電導性流体の管内振動流れII 平行平面完全導体壁間内の場合

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